Finding

In the expression , the radicand is a perfect square. It is tempting to think

that = a, but we see below that this is not the case.

Suppose a = 5. Then we have , which is , or 5.

Suppose a = -5. Then we have ,which is , or 5.

Suppose a = 0 . Then we have which is , or 0.

The symbol never represents a negative number. It represents the

principal square root of a^{2}. Note the following.

**SIMPLIFYING **

a ≥ 0 = a

if a is positive or 0 ,the principal square root of is a.

a < 0 = -a

If a is negative, the principal square root of is the opposite of a.

In all cases, the radical expression represents the absolute value of *a*.

**PRINCIPAL SQUARE ROOT OF a ^{2}**

For any real number a, = \left | a \right | . The principal (nonnegative) square

root of a^{2} is the absolute value of a.